The dimensions of a rectangular prism are shown below: Length 2 1/4 ft | width 1 ft | height 1 1/4 ft.

The lenghts of the sides of a small cube are 1/4 ft each.

Part A: how many small cubes can be packed in the rectangular prism? Show your work. (5 Points)
Part B: Use the asnwer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 Points)​

Solution :

Let the revenue be = R

Therefore, R = price x quantity

                  R = (30 - 2x) ( 5000 + 500x)

                     = [tex]150000 + 5000x - 1000x^2[/tex]

For the maximum revenue,

[tex]$\frac{dR}{dx} = 0$[/tex]

[tex]$-2000x+5000=0$[/tex]

[tex]$x=2.5$[/tex]

[tex]$\frac{d^2R}{dx^2}=-2000<0$[/tex]

At [tex]x=2.5[/tex], the revenue is maximum.

So the price for the maximum company revenue = [tex]$30-2x$[/tex]

                                                                                  [tex]$=30-2(2.5)$[/tex]

                                                                                  = 30 - 5

                                                                                  = 25

Therefore, the price that will maximize the company's revenue is $25.

Answer:

number is 6

Step-by-step explanation:

let the number be x , then double the number is 2x and

2x - [tex]\frac{1}{3}[/tex] x = 10 ( multiply through by 3 to clear the fraction )

6x - x = 30

5x = 30 ( divide both sides by 5 )

x = 6

That is the number is 6

Answer:

6

Step-by-step explanation:

how often is that question posted here ?

this means that we need to find the value of x, so that the functional (result) value is 7.

7 = (3x - 4)/2

14 = 3x - 4

18 = 3x

x = 6

Answer:[tex]1651.38\ ft[/tex]

Step-by-step explanation:

Given

A walking trail is [tex]1580.76\ ft[/tex] long and a lake is located [tex]70.62\ ft[/tex] away  from end  of the trail

The distance from the start of the trail to the lake is the sum of the length of the trail and lake

[tex]\Rightarrow 1580.76+70.62\\\Rightarrow 1651.38\ ft[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Decreasing rate = 12% = 0.12

y = 2400 * (1- 0.12)^x = 2400*(0.88)^x

x = 8 years

[tex]y = 2400 *(0.88)^{8}\\\\= 2400*0.36\\\\= 863[/tex]

Answer:

4x-7y = -21

Step-by-step explanation:

1. Move 4/7x to the other side

-4/7x+y=-3

2. Multiply both sides by -7

4x-7y=-21

3x-7y=28 is it in standard form

[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]

Answer:

24aprtment3

Step-by-step explanation:

Answer: d. alternate interior angles

Note how the two angles are inside, or interior, of the lines L1 and L2. For me, I tend to think of such lines like train tracks. So that takes care of the "interior" portion.

As for the "alternate" portion, we can see that the angles are on either side of the transversal line T.

So that's why angles 3 and 6 are alternate interior angles.

If L1 and L2 are parallel, then angle 3 = angle 6.

The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.

Answer:

Step-by-step explanation:

Given :

45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44

Using technology, the box and whisker plot generated for the data is attached below.

The 5 - number summary is also given below :

Minimum: 39

Median: 45

First quartile: 42

Third quartile: 47

Interquartile Range: 5

Maximum: 49

Outliers: none

Answer:

Step-by-step explanation:

Answer:

a)11cm

b)49.5cm²

Step-by-step explanation:

to find the perimeter you use the formula

o/360×2piR

since 2pi R=18pi cm,to find the radius you cancel pi from both sides 2r/2=18/2...so the radius is 9cm

therefore the perimeter will be:

70/360×2×22/7×9

27720/2520

=11cm

then to find the area you say

o/360×pi R²

70/360×22/7×9²

124740/2520

=49.5cm²

I hope this helps

Answer:

see below

Step-by-step explanation:

3x + 5 = 17

Subtract 5 from each side

3x+5-5 = 17-5

3x = 12

Divide each side by 3

3x/3 =12/3

x =4

Answer:

B (x=4)

Step-by-step explanation:

plug it in...

3(4)+5=17

Answer:

Functions can be symmetrical about the y-axis, which means that if we reflect their graph about the y-axis we will get the same graph. ... These are two types of symmetry we call even and odd functions.

Step-by-step explanation:

Answer:

The given polynomial is,

2x³+5x²-8x-10=0

all possible roots of a polynomial,

ax³+b²+c x +d=0 ← all possible factors of ration (d/a)

Therefore, eq (1), all possible factors are the factors of ratio (-10/2)

which are, B) { ± 1, 1/2, ± 2, ± 5/2, ±5, ± 10}

OAmalOHopeO

Answer:

domain [-1, ∞)

range [ -3, ∞)

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

It's a 45-45-90 triangle, it has two similar sides, since it has two similar angles, which are both 45°

so, side = s = 6

Answered by GAUTHMATH

The length of the leg s of the triangle below is 6.

Option D is the correct answer.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Applying the Pythagorean theorem in the triangle.

√72² = s² + 6²

72 = s² + 36

s² = 72 - 36

s² = 36

s = √36

s = 6

We can also say that,

Opposite angles of equal sides are equal

So,

s = 6.

Thus,

The length of the leg s of the triangle below is 6.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ7

Answer:

8.2 units

Step-by-step explanation:

For radioactive decay, the amount should decrease over time. Given the function:

f(x) = 10(0.98[tex])^{x}[/tex]

We substitute the time of x = 10 hours:

f(10) =  10(0.98[tex])^{10}[/tex]

f(10) = 8.17

Round 8.17 to 8.2.

Therefore 8.2 units will remain after 10 hours.

Answer:

Step-by-step explanation:

from the picture:

QP = QR

and

QR = RS

so

PQ + RS = QS

Answer:

This is trapezium.

Area of this figure =1/2h(d1-d2)

1/2×5(14-8)

=30/2

=15cm^2

Answer: -2/7

|3x - 2| - 4x = 4

1) (3х - 2) - 4х = 4, if 3x - 2 >= 0

2) -(3x - 2) - 4x = 4, if 3x - 2 < 0

1)

3х - 4х = 4 + 2

-x = 6

x = -6

3х - 2 >= 0

3х >= 2

x >= 2/3 - wrong

2)

-3х + 2 - 4х = 4

-7х = 2

x = -2/7

3x-2<0

3x<2

3(-2/7)<2-right

Use main properties of powers

(a^m)^n=a^{m\cdot n};(am)n=am⋅n;

\dfrac{1}{a^n}=a^{-n}an1=a−n

to simplify given equation.

1.

4^x=(2^2)^x=2^{2x}.4x=(22)x=22x.

2.

\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.(81)x+5=(231)x+5=(2−3)x+5=2−3x−15.

3. Then the equation is

2^{2x}=2^{-3x-15}.22x=2−3x−15.

The bases are the same, so equate the powers:

2x=-3x-15,

2x+3x=-15,

5x=-15,

x=-3.

Answer: for x=-3.

Answer:

A the first one.

Step-by-step explanation:

Wy = 28

WX = 12

XY = WY - WZ

XY = 28 - 12

XY = 16

4P = 16

P = 16/4

P = 4

Answer:

it took 7 boys 21 days to clear a piece of land.

Answer:

C

Step-by-step explanation:

Given

10(3x + 2) > 7(2x - 4) ← distribute parenthesis on both sides

30x + 20 > 14x - 28 ( subtract 14x from both sides )

16x + 20 > - 28 ( subtract 20 from both sides )

16x > - 48 ( divide both sides by 16 )

x > - 3 → C

Phase shift and period change

Rewriting the equation:

y = cos ( 2 ( x - 2 ) )

Phase shift 2 units to the right

Period changed to 2pi/2 = pi

Answer:

4

Step-by-step explanation:

(21 + 5) : 2 = 13

(7 + 9) : 2 = 8

(36 + 2) : 2 = 19

(1 + 7) : 2 = 4

Answer:

y = -6x + 6

Step-by-step explanation:

The general equation of a line is

y = mx + b

where m is the slope and b is the y-intercept

The slope in the first equation is 1/6

Mathematically, when two lines are perpendicular, the product of their slopes is -1

1/6 * m2 = -1

m2 = -6

So we have the equation as;

y-y1 = m(x-x1)

y-23 = -6(x + 3)

y = -6x -18 +23

y = -6x + 6

Answer:

C

Step-by-step explanation:

There isn’t one

Answer:

13/9

Step-by-step explanation:

Given

5/9 + 8/9

Both fractions have the same denominator.

Therefore, pick one of the denominator and add the numerators

5/9 + 8/9

= (5+8) / 9

= 13/9

5/9 + 8/9 = 13/9

Answer:

1/8 rooms per hour

Step-by-step explanation:

We are given that Beatrice can wallpaper 1 room in 8 hours. The work rate is how many rooms Beatrice can wallpaper in one unit of time (in this case, one hour).

Another way of saying 1 room in 8 hours is 1 room/8 hours. We want to find the rate over one hour, so we want to make the denominator ( in hours) equal to 0.

With fractions, we can divide/multiply both the numerator and denominator by the same amount, and still keep the fraction. Therefore, we want to make 8 hours 1 hour by multiplication or division. Since anything divided by itself is equal to 1, we can say that 8/8 is equal to 1. Therefore, we can divide both the numerator and denominator by 8 to get

(1 room/8) = (8 hours / 8)

= (1/8 rooms) / 1 hour

Therefore, the work rate is 1/8 rooms per hour